Potential
Potential is a mechanic added in version 1.1.0. It acts as a representative value of the player's best and recent performances. It generally does not affect gameplay, with the following few exceptions: * Unlocking World Mode Map 2-3 (see Singularity § Challenge) * Unlocking SAIKYO STRONGER's Future chart Playing songs while online will affect this value, displayed on the icon of your partner at the top of the screen. Ranks There are eight different icons for your Potential rating, seven of them representing distinct potential ranges. There is also a special icon for those who have "Show Potential" disabled under Settings. As potential is strongly dependent on which songs are owned and inflates upon the release of new song packs, descriptions become obsolete over time and are hence not provided. Mechanics Early research credit goes to choka_noah and is posted here with their permission. There are several relevant quantities to the Potential: * Chart Constant - a value inherent to a chart, rounded to the nearest 1 decimal point. * Score Modifier - a value based on score. * Chart Potential - a value obtained by adding the Chart Constant and Score Modifier, lower-bounded at 0. * Recent Entries - a list of 10 plays with the highest chart potential, out of the 30 most recent plays (charts can appear more than once, hence "plays"). * Best Entries - a list of 30 unique charts with the highest chart potential obtained on, of all time (charts can only appear once). Potential is the average of the 40 total chart potentials in recent entries and best entries. It is displayed up to two decimal points, with any more being truncated. There are 2 special cases wherein Potential cannot decrease: * Obtaining EX rank. * Losing in the middle of a song due to the HARD skill effect. Plays falling under any of these situations are only updated in the recent entries if they cause an increase in Potential. As such, the approach to maximize one's Potential is to: * Avoid grades below EX when online (for recent entries). * Maximize score in songs with higher chart constants (for best entries). Chart Constant The chart constant is an internal value assigned to a song, which is a more precise representation of its difficulty than its difficulty level. It is currently unknown how these values are determined or calculated. Chart constants for various songs, as well as the methods used to obtain these values, are detailed in Songs by Chart Constant. In addition to determining Potential gain/loss from a song, they also determine how much Steps are gained when completing songs in World Mode. As chart constants are stored on the online server, Potential does not change and World Mode is inaccessible when not connected. Score Modifier The score modifier is a value computed from your score. It can be positive (reward) or negative (penalty), depending on whether your score is above or below 9,500,000. For a score of 9,500,000, the score modifier is exactly zero. Below is a table showing the formula for calculating the score modifier for various score ranges. Below are score modifiers for some notable scores: Chart Potential The chart potential, known internally as rating, is an intermediate value used to calculate the potential. It is simply the sum of the chart constant and the score modifier, and rectified to become zero if the result is negative. \text{Chart Potential}=\max\{\text{Chart Constant}+\text{Score Modifier},0\} For example, Sayonara Hatsukoi FTR has a chart constant of 6.5, so if you obtain a Pure Memory, the corresponding score modifier is 2.0. This results in a chart potential is 8.5 which gets saved in your recent/best entries. Maximum Potential Calculation In order to attain the maximum Potential, you need to have the highest possible chart potential for best entries and recent entries. Best Entries: Since chart potentials in best entries are limited to one per song, one can maximise the best entries by obtaining a Pure Memory on 30 charts with the highest chart constants: The total chart constant of these songs is 313.5, which results in a maximum best entries total of: 313.5 + 2.0 \times 30 = 373.5 Recent Entries: Since chart potentials in recent entries are not limited to one per song, one can maximise the recent entries by obtaining a Pure Memory on Grievous Lady FTR 10 times. This results in a maximum recent entries total of: \bigl\text{ (Chart Constant)} + 2.0 \text{ (Score Bonus)}\bigr \times 10 \text{ (Plays)} = 132.0 Result: Adding the total recent Potential and the total best Potential, then dividing by 40 and rounding down gives: \frac{373.5 + 132.0}{40} \approx 12.63 This yields the highest possible Potential one can currently obtain: 12.63. History This section lists the maximum possible Potential on every version of Arcaea where new songs were added. The values for versions before the potential system was introduced (1.1.0) are also shown here. The "Minimum CC" is the lowest Chart Constant that affected the maximum potential in each version. Gallery potential down.png|Potential down, keep and up (credit to the Japanese wiki) method_1.jpg|Derive chart constant by method 1 (credit to the Japanese wiki) potential_rating.png|Potential ranks (credit to the Japanese wiki) Potential.jpg|Potential ranks (including comparisons with pre 1.5 system, credit to the Japanese wiki) Category:Game Mechanics